Index

Abstract

In this paper improved evolutionary algorithm (IEA) and enriched firefly algorithm (EFA) has been used to solve optimal reactive power problem. In the improved evolutionary algorithm by using the set of route vectors the search has been enhanced and in the enriched firefly algorithm differential evolution algorithm has been mingled to improve the solution. Both the proposed IEA&EFA has been tested in practical 191 (Indian) utility system and simulation results show clearly about the better performance of the proposed algorithm in reducing the real power loss with control variables within the limits.

1. Introduction

To till date various methodologies had been applied to solve the Optimal Reactive Power problem. The key aspect of solving Reactive Power problem is to reduce the real power loss. Previously many types of mathematical methodologies like linear programming, gradient method (Alsac and Scott, 1973; Hobson, 1980; Lee et al., 1985; Monticelli et al., 1987; Deeb and Shahidehpur, 1990; Lee et al., 1993; Mangoli and Lee, 1993; Canizares et al., 1996) has been utilized to solve the reactive power problem, but they lack in handling the constraints to reach a global optimization solution. In the next level various types of evolutionary algorithms (Eleftherios et al., 2010; Hu et al., 2010; Berizzi et al., 2012; Roy et al., 2012) has been applied to solve the reactive power problem. But each and every algorithm has some merits and demerits. This paper proposes improved evolutionary algorithm (IEA) and enriched firefly algorithm (EFA) to solve optimal reactive power problem. In the improved evolutionary algorithm by using the set of route vectors the search has been enhanced and in the enriched firefly algorithm differential evolution algorithm has been mingled to improve the solution. Both the proposed IEA&EFA has been tested in practical 191 (Indian) utility system. The simulation results show that the proposed approach outperforms all the entitled reported algorithms in minimization of real power loss.

2. Objective Function

2.1.Active Power Loss

The objective of the reactive power dispatch problem is to minimize the active power loss and can be defined in equations as follows:

2.2. Voltage Profile Improvement

2.4. Inequality Constraints

3. Improved Evolutionary Algorithm (IEA)

Solutions are more to be anticipated to be designated to create new-fangled solutions, and then their sub objective spaces can quickly find their optimal solutions. In order to attain the goalmouth, the crowding distance is used to calculate the fitness value of a solution for the selection operators. Since these solutions are controlled by other solutions and the objective vectors of those solutions do not locate in this sub objective spaces of these solutions, so in the term of the objective vector, these solutions have rarer solutions in their frame than other solutions. Thus, by using the crowding distance to calculate the fitness value of a solution, the fitness values of these solutions are better than those solutions and these solutions are more likely to be designated to create new-fangled solutions

4. Enriched Firefly Algorithm (EFA)

Where and are uniformly distributed random values between 0 to 1. Thus, the updated attractiveness values assisted the population to move towards the solution that produced the current best fitness value .

On the other hand, the second sub-population contained solutions that produced less significant fitness values. The solutions in this population were subjected to undergo the evolutionary operations of DE method. Firstly, the trivial solutions were produced by the mutation operation performed on the original counterparts. The ith trivial solution, , was generated based on the following equation:

5. Simulation Study

Both algorithms have been tested in practical 191 test system and the following results has been obtained

In Practical 191 test bus system – Number of Generators = 20, Number of lines = 200, Number of buses = 191 Number of transmission lines = 55. Table 1&2 shows the optimal control values of practical 191 test system obtained by IEA and EFA methods. And table 3 shows the results about the value of the real power loss by obtained by both proposed improved evolutionary algorithm and enriched firefly algorithm. Although both the projected algorithms successfully applied to the problem IEA has the edge over EFA in reducing the real power loss.

Table-1. Optimal Control values of Practical 191 utility (Indian) system by IEA method

6. Conclusion

In this paper, both the improved evolutionary algorithm and enriched firefly algorithm has been successfully implemented to solve Optimal Reactive Power Dispatch problem. The proposed algorithms have been tested in practical 191 (Indian) utility system. Simulation results show the robustness of proposed algorithms for providing better optimal solution in decreasing the real power loss. The control variables obtained after the optimization by both algorithms are well within the limits.